Minimax Robust Matched Filters for Noise Uncertainty Within 2- Alternating Capacity Classes.
Geraniotis, Evaggelos A.
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In this paper, we address the problem of designing matched filters which are robust against uncertainty in the statistics of the noise process. The design is based on a game-theoretic approach in which a filter is sought that has the maximum worst- case output signal-to-noise ratio possible over the class of allowable statistics, that is the design is maximin signal-to- noise ratio. The problem is formulated and solved for both discrete-time and continuous-time matched filters with uncertainty in either the autocorrelation function or the spectral measure of the noise. For uncertainty models determined by 2-alternating Choquet capacities explicit solutions are obtained which are characterized by the Huber-Strassen derivative of the capacity generating the class with respect to a Lebesgue- like measure on a suitable interval.